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Risk Measures. CARE Meeting Hamilton, Bermuda June 6-7, 2005. Paul Kneuer, FCAS MAAA, Holborn Corporation Susan Patschak, FCAS MAAA, Endurance Specialty. Risk Measures. Why do different reinsurers often make different decisions when it comes to pricing the same risk?

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risk measures

Risk Measures

CARE Meeting

Hamilton, Bermuda

June 6-7, 2005

Paul Kneuer, FCAS MAAA, Holborn Corporation

Susan Patschak, FCAS MAAA, Endurance Specialty

risk measures1
Risk Measures
  • Why do different reinsurers often make different decisions when it comes to pricing the same risk?
  • Different reinsurers have different measures of profitability.

2

risk measures2
Risk Measures
  • Possible measures
  • Contract Profit/Contract Premium
  • Contract Profit/Contract Standard Deviation
  • Contract Profit/Contribution to Portfolio Std Dev
  • Contract Profit/Contract TCE or TVar
  • Contract Profit/Contract PML
  • Contract Profit/Contribution to Portfolio PML

3

risk measures3
Risk Measures

The following four contracts will be used to compare different risk measures:

  • Net Account Quota Share
  • Umbrella Cessions Facility
  • Catastrophe XOL
  • Catastrophe XOL in a Peak Zone

4

risk measures4
Risk Measures

Risk Measures used for the first two contracts

  • Risk Measure: Contract Profit/Contract Premium
    • Used by companies constrained by premium-to-surplus ratios
    • Analogous measures: Combined ratio, Operating ratio
  • Risk Measure: Contract Profit/Contract Standard Deviation
    • Used by companies that are constrained by operating volatility, and that cannot give contracts credit for diversification — due to correlation or large contract size.
    • Analogous Measures: Rate on-line, Value at Risk

5

risk measures5
Risk Measures

Net Account Quota Share

  • Terms
    • $50Mn expected ceded premium
    • $1Mn occurrence cap
    • Expected profit of $2Mn, after sliding scale commission. (Remember them?)
    • Standard Deviation of returns is $4Mn

6

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Risk Measures

Net Account Quota Share

  • Risk Measure: Contract Profit/Contract Premium

$2Mn/$50Mn = 4%

Conclusion: Well below average. Should decline.

  • Risk Measure: Contract Profit/Contract Std Dev

$2Mn/$4Mn = 50%

Conclusion: Well above average. Should write.

7

risk measures7
Risk Measures

Umbrella Cessions Facility

  • Terms
    • $5Mn expected ceded premium
    • $10Mn per policy limit
    • Expected profit of $2Mn, after PC
    • Standard Deviation of returns is $20Mn

8

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Risk Measures

Umbrella Cessions Facility

  • Risk Measure: Contract Profit/Contract Premium

$2Mn/$5Mn = 40%

Conclusion: Well above average. Should accept.

  • Risk Measure: Contract Profit/Contract Std Dev

$2Mn/$20Mn = 10%

Conclusion: Well below average. Should decline.

9

risk measures9
Risk Measures

Risk Measures used for the next two contracts

  • Risk Measure: Contract profit/Consumption of allocated capital

= return on allocated capital (ROAC), or

= risk adjusted return on capital (RAROC)

  • Risk Measure: Contract Profit/Contract ROL
  • Risk Measure: Contract Profit/Contract CR
  • Company A: uses RM 1 & 3
  • Company B: uses RM 2 & 3

10

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Risk Measures

Catastrophe XOL

  • Terms
    • Ceded premium = $390,000
    • Limit = $8.2 million
    • Losses and Expenses = $318,000
    • Profit = $ 72,000
    • Allocated capital = $101,000

11

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Risk Measures

Catastrophe XOL

  • ROAC = 71.3%
  • ROL = 4.7%
  • Combined Ratio = 81.5%
  • What decision does Company A make versus Company B? Why?

12

risk measures12
Risk Measures

Catastrophe XOL in Peak Zone

  • Terms
    • Ceded premium = $335,000
    • Limit = $1.675 million
    • Losses and Expenses = $235,000
    • Profit = $100,000
    • Allocated capital = $1 million

13

risk measures13
Risk Measures

Catastrophe XOL in Peak Zone

(e.g. Japan, Florida, UK)

  • ROAC = 10%
  • ROL = 20%
  • Combined Ratio = 70%
  • What decision does Company A make versus Company B? Why?

14

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Risk Measures

What else needs consideration?

  • Standalone?
  • Perils?
  • Claims department vs. Independent claims adjusters?
  • Resolution quality of exposure data?
  • ITV undervaluation?
  • Client relationship to producers?

15

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Risk Measures

Catastrophe Quota Share

  • Attritional loss ratio
  • Catastrophe load factor
  • Client operations/structure
  • Data quality both exposure and experience

16

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Risk Measures

ObservationsUnderwriters’ Preferences by Risk Measure

  • Profit/Allocated Capital
  • Contracts withoutinuring protections
  • Excess
  • High layers
  • Catastrophe Coverage
  • Profit/SD
  • Net placements
  • Pro-Rata
  • Low layers
  • Working Coverage

17

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